Cooper pair formation in U(1) gauge theory of high temperature superconductivity

We study the two-dimensional spin-charge separated Ginzburg-Landau (GL) theory containing U(1) gauge interactions as a semi-phenomenological model describing fluctuating condensates in high temperature superconductivity. Based on the original GL action, we derive the effective action of Cooper pair. Especially, we clarify how Cooper pair correlation evolves in the normal state from the point of view of spin-charge separation. Furthermore, we show how Cooper pair couples to gauge field in a gauge-invariant way stressing the insensitivity of Cooper pair to infrared gauge field fluctuation.